Radial Symmetry in Editing a Single Object
I would do this using the Array modifier, which can replicate a radial mirror.

First, lets say I have some portion of my object that i want to revolve around the origin:



I then add an Array Modifier, and set the count to how many copies I want (in this case 6, in your case 8):



Then, add an empty to your scene. Remove the relative offset on your array modifier, and check the object offset button, and choose your empty at the origin:



Then, as you rotate your empty around the z axis, you will notice the array copies will rotate with it (make sure both the empty and the object are centered on the origin for this).

With 6 copies in total, I want each copy to be 360/6 = 60 degrees apart, so I will press R Z 60 to rotate my empty 60 degrees, giving me the following result:



Now, I can just edit one part of the hexagon, and the rest will be mirrored automatically:



I hope this helps!